Two particles P and Q have mass 0.4 kg and 0.6 kg respectively. The particles are initially at rest on a smooth horizontal table. Particle P is given an impulse of magnitude 3 N s in the direction PQ. (a) Find the speed of P immediately before it collides with Q. Immediately after the collision between P and Q, the speed of Q is 5 m s -1 . (b) Show that immediately after the collision P is at rest.

A-Level Edexcel Maths Mechanics Further Forces & Newtons Laws: Two particles P and Q have mass

Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Question 1

Two particles P and Q have mass 0.4 kg and 0.6 kg respectively. The particles are initially at rest on a smooth horizontal table. Particle P is given an impulse of m... show full transcript

Worked Solution & Example Answer:Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Step 1

Find the speed of P immediately before it collides with Q.

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Answer

To find the speed of particle P before the collision, we can use the impulse-momentum theorem, which states that the impulse (I) equals the change in momentum (mv).

Given that:

Mass of P, $m = 0.4$ kg
Impulse, $I = 3$ N s

Using the formula: $I = m v$ Substituting the values: $3 = 0.4 v$

Solving for $v$ : $v = rac{3}{0.4} = 7.5 ext{ m/s}$

Thus, the speed of P immediately before it collides with Q is 7.5 m/s.

Step 2

Show that immediately after the collision P is at rest.

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Answer

Immediately after the collision, we know from the question that the speed of Q is 5 m/s.

Using the principle of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision:

Before collision:

Momentum of P: $0.4 imes 7.5 = 3$ kg·m/s
Momentum of Q: $0.6 imes 0 = 0$ kg·m/s

Total momentum before: $3 + 0 = 3$ kg·m/s

After collision (let the speed of P be $v$ ):

Momentum of P: $0.4 v$
Momentum of Q: $0.6 imes 5 = 3$ kg·m/s

Total momentum after: $0.4v + 3$

Setting the total momentum before and after equal: $3 = 0.4v + 3$ Solving for $v$ : $0.4v = 0$ $v = 0$ Thus, particle P is at rest immediately after the collision.

Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Worked Solution & Example Answer:Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Find the speed of P immediately before it collides with Q.

Show that immediately after the collision P is at rest.

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